Some results on star-line graphs

Abstract

"Let $H$ be a connected graph with at least three vertices. The $H$-line graph, $HL(G)$, of a graph $G$ has all the edges of $G$ as its vertices, two vertices of $HL(G)$ are adjacent if the corresponding edges in $G$ are adjacent and belong to a common copy of $H$. In this paper we investigate some properties of the star-line graph $K_{1,n}L(G)$ of a graph $G$. We also obtain a Krausz type characterization for star-line graphs. Traversability of star-line graphs is also studied."